Theorems · Theorem · order theory

smul_lt_smul_iff_of_neg_left

∀ {α : Type u_1} {β : Type u_2} {a : α} {b₁ b₂ : β} [inst : Ring α] [inst_1 : PartialOrder α] [IsOrderedRing α]
  [inst_3 : AddCommGroup β] [inst_4 : PartialOrder β] [IsOrderedAddMonoid β] [inst_6 : Module α β]
  [PosSMulStrictMono α β] [PosSMulReflectLT α β], a < 0 → (a • b₁ < a • b₂ ↔ b₂ < b₁)

Defined in

Mathlib.Algebra.Order.Module.Defs

Cited by

4 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingPartialOrderIsOrderedRingAddCommGroupPartialOrderIsOrderedAddMonoidModulePosSMulStrictMonoPosSMulReflectLT